Question

rewrite the expression $csc(90^{circ}-\theta)sin\theta$ as one of the six trigonometric functions of acute angle $\theta$.

Explanation:

Step1: Use co-function identity

$\csc(90^\circ-\theta)=\sec\theta$

Step2: Rewrite secant as reciprocal cosine

$\sec\theta=\frac{1}{\cos\theta}$

Step3: Substitute and simplify expression

$\frac{1}{\cos\theta}\cdot\sin\theta=\frac{\sin\theta}{\cos\theta}$

Step4: Use tangent identity

$\frac{\sin\theta}{\cos\theta}=\tan\theta$

Answer:

$\tan\theta$